Although the present invention may have application in forming contoured surfaces on a wide variety of materials, and for widely diverse uses, the concepts of the invention can be clearly understood by an explanation which relates to the usage of the invention to form a backrest cushion for a human. Once the concepts of the invention are understood in their application to the fabrication of backrest cushions, those concepts can be readily adapted to the forming of contoured surfaces on a wide variety of materials for numerous purposes.
Backrests, and particularly those adapted to support the lumbar region as well as the lateral sides of the torso, present a highly complex, contoured surface which curves convexly in a vertical orientation to support the lumbar arch and at the same time curves concavely in a transverse orientation to conform with, and support, the lateral sides of the torso. In mathematical terminology the geometry of the aforesaid backrest surface is a hyperbolic paraboloid. An understanding as to how a linear cutting device can form a hyperbolic paraboloid according to the concepts of the present invention will allow those skilled in the art to adapt the present invention to other purposes.
The typical backrest support cushion is often formed from an expanded cellular foam so that it will be soft and pliable, even though it does have a supporting surface which is convexly curved to conform to the lumbar arch and two wing surfaces adapted to engage the lateral sides of the torso.
Backrest cushions have historically been formed by molding or by a combined deformation and cutting process. In the molding process a separate and distinct mold is required for each size cushion as well as for cushions of the same size having variations in the curvature, or other dimensions, of the lumbar supporting region and/or variations in the curvature, or other dimensions, of the laterally spaced wing portions adapted to engage the sides of the torso. For example, it may be desirable to provide a more or less pronounced curve for supporting the lumbar arch or to provide the cushion with a lumbar supporting region that is not sagittally oriented--i.e., a lumbar supporting region that is tilted in one direction or another from the central, sagittal plane. Each such variation requires a separate and distinct mold. Thus, a large inventory of expensive molds must be maintained to provide even the most routine variations, and, because of normal wear and tear, it is necessary to replace the molds for the more popular cushions from time to time thereby further adding to the expense of the molding process.
In addition to the molds themselves, the machines by which the molds are operated are themselves intricate devices which are not only expensive to manufacture but also to maintain, adding still further to the expense of the molding process. Another drawback of the molding process is that only one cushion can be produced per mold cavity during the time cycle of the molding process.
The deformation and cutting process involves the use of complicated, preformed, and opposed, dies to compress a block of resilient material to varying degrees according to a predetermined complex pattern so that when the block is compressed and then cut transversely between the dies, the material will expand to the desired shape across the full face of each parting surface after the pressure of the dies has been released. As should be apparent, it is an extremely complicated process even to design the pattern of the compressing surfaces on the dies so that the required selective compression of the block will be accomplished. Moreover, accuracy will depend upon the consistency of the material from which the block is made, and any block-to-block variation in the resilience of the material, or even spot-to-spot variations within a block, will result in inaccurately contoured surfaces. As such, it is quite difficult to replicate a particular shape from run to run with different lots, or stocks, of resilient material, and impossible to use the compression and cutting process on a non-resilient material. Obviously, therefore, the deformation and cutting process also requires a distinct pair of opposed dies for each size and each shape of backrest cushion. Thus, the die inventory cost disadvantage for the compression and cutting process is comparable to the mold inventory cost disadvantage of the molding process. Here, too, a machine is required to compress a block of material positioned between the opposed dies. As with the molding process, the initial investment and upkeep of the machines and dies for the compression and cutting process is significant and results in increased cost for a cushion made by that process.